837 research outputs found
The PCA-seq method applied to analyze of the dynamics of COVID-19 epidemic indicators
In time series analysis using the SSA method, a univariate series is converted into the multivariate one by shifts. The resulting trajectory matrix is subjected to principal component analysis (PCA). However, the principal components can also be computed using the PCA-Seq method if segments of the original series are selected as objects. The matrix of Euclidean distances between the objects can be obtained using any method, which offers additional opportunities for time series analysis compared to the conventional SSA. In this study, the PCA-Seq method was used to analyze the dynamics of COVID-19 epidemic indicators
Integrable magnetic geodesic flows on Lie groups
Right-invariant geodesic flows on manifolds of Lie groups associated with
2-cocycles of corresponding Lie algebras are discussed. Algebra of integrals of
motion for magnetic geodesic flows is considered and necessary and sufficient
condition of integrability in quadratures is formulated. Canonic forms for
2-cocycles of all 4-dimensional Lie algebras are given and integrable cases
among them are separated.Comment: 16 page
Regularization of a three-body problem with zero-range potentials
We propose a coordinate-space regularization of the three-body problem with
zero-range potentials. We include the effective range and the shape parameter
in the boundary condition of the zero-range potential. The proposed extended
zero-range model is tested against atomic helium trimers and is shown to
provide an adequate quantitative description of these systems
Differential Form of the Skornyakov--Ter-Martirosyan Equations
The Skornyakov--Ter-Martirosyan three-boson integral equations in momentum
space are transformed into differential equations. This allows us to take into
account quite directly the Danilov condition providing self-adjointness of the
underlying three-body Hamiltonian with zero-range pair interactions. For the
helium trimer the numerical solutions of the resulting differential equations
are compared with those of the Faddeev-type AGS equations.Comment: 4 pages, 2 figure
Efimov states in atom-molecular collisions
We analyse scattering of a heavy atom off a weakly bound molecule comprising
an identical heavy and a light atom in the Born-Oppenheimer approximation. We
focus on the situation where the heavy atoms are bosons, which was realized in
several experiments. The elastic and inelastic cross sections for the
atom-molecular scattering exhibit a series of resonances corresponding to
three-body Efimov states. Resonances in elastic collisions are accessible
experimentally through thermalization rates, and thus constitute an alternative
way of observing Efimov states.Comment: 4 pages, 2 figure
Collisional relaxation of Feshbach molecules and three-body recombination in 87Rb Bose-Einstein condensates
We predict the resonance enhanced magnetic field dependence of atom-dimer
relaxation and three-body recombination rates in a Rb Bose-Einstein
condensate (BEC) close to 1007 G. Our exact treatments of three-particle
scattering explicitly include the dependence of the interactions on the atomic
Zeeman levels. The Feshbach resonance distorts the entire diatomic energy
spectrum causing interferences in both loss phenomena. Our two independent
experiments confirm the predicted recombination loss over a range of rate
constants that spans four orders of magnitude.Comment: 4 pages, 3 eps figures (updated references
3D-4D Interlinkage Of qqq Wave Functions Under 3D Support For Pairwise Bethe-Salpeter Kernels
Using the method of Green's functions within a Bethe-Salpeter framework
characterized by a pairwise qq interaction with a Lorentz-covariant 3D support
to its kernel, the 4D BS wave function for a system of 3 identical relativistic
spinless quarks is reconstructed from the corresponding 3D form which satisfies
a fully connected 3D BSE. This result is a 3-body generalization of a similar
2-body result found earlier under identical conditions of a 3D support to the
corresponding qq-bar BS kernel under Covariant Instaneity (CIA for short). (The
generalization from spinless to fermion quarks is straightforward).
To set the CIA with 3D BS kernel support ansatz in the context of
contemporary approaches to the qqq baryon problem, a model scalar 4D qqq BSE
with pairwise contact interactions to simulate the NJL-Faddeev equations is
worked out fully, and a comparison of both vertex functions shows that the CIA
vertex reduces exactly to the NJL form in the limit of zero spatial range. This
consistency check on the CIA vertex function is part of a fuller accounting for
its mathematical structure whose physical motivation is traceable to the role
of `spectroscopy' as an integral part of the dynamics.Comment: 20 pages, Latex, submitted via the account of K.-C. Yan
Spectropolarimetry of R Coronae Borealis in 1998--2003: Discovery of Transient Polarization at Maximum Brightness
We present an extended optical spectropolarimetry of R CrB from 1998 January
to 2003 September. The polarization was almost constant in the phase of maximum
brightness, being consistent with past observations. We detected, however,
temporal changes of polarization ( %) in 2001 March and August, which
were the first detection of large polarization variability in R CrB near
maximum brightness. The amplitude and the position angle of the `transient
polarization' were almost constant with wavelength in both two events. There
was a difference by about 20 degrees in the position angle between the two
events. Each event could be explained by light scattering due to short-lived
dust puff occasionally ejected off the line of sight. The flatness of the
polarization against the wavelength suggests that the scatterer is a mixture of
dust grains having various sizes. The rapid growth and fading of the transient
polarization favors the phenomenological model of dust formation near the
stellar photosphere (e.g., within two stellar radii) proposed for the time
evolution of brightness and chromospheric emission lines during deeply
declining periods, although the fading timescale can hardly be explained by a
simple dispersal of expanding dust puff with a velocity of km s
. Higher expansion velocity or some mechanism to destroy the dust grains
should be needed.Comment: 22 pages, 10 figures, accepted for publication in A
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